Q 35. - Calculus

Question

Find the norm of the vector. $v=\left(\frac{1}{3},\frac{1}{3},-\frac{1}{3}\right)$

Step-by-Step Solution

Answer

The norm of the vector $v=\left(\frac{1}{3},\frac{1}{3},-\frac{1}{3}\right)$ is $\sqrt{\frac{1}{3}}$.

Step 1. Given information .

We have given vector $v=\left(\frac{1}{3},\frac{1}{3},-\frac{1}{3}\right)$.

Step 2. Find the norm of the vector.

$$\begin{gathered} ||v||=\sqrt{a^2+b^2+c^2} \\ =\sqrt{{\left(\frac{1}{3}\right)}^2+{\left(\frac{1}{3}\right)}^2+{\left(\frac{1}{3}\right)}^2} \\ =\sqrt{\frac{1}{9}+\frac{1}{9}+\frac{1}{9}} \\ =\sqrt{\frac{3}{9}} \\ =\sqrt{\frac{1}{3}} \end{gathered}$$